Least Common Multiple (LCM) of 199 and 25
The least common multiple (LCM) of 199 and 25 is 4975.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 199 and 25?
First, calculate the GCD of 199 and 25 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 25 = 7 remainder 24 |
| 2 | 25 ÷ 24 = 1 remainder 1 |
| 3 | 24 ÷ 1 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 81 | 1053 |
| 174 and 80 | 6960 |
| 140 and 80 | 560 |
| 179 and 73 | 13067 |
| 113 and 155 | 17515 |